Transcript Chapter 15: Vibrations and Waves

Chapter 15:
Vibrations and Waves
Rebecca, Michelle, Anders, Luke
Chapter Summary
• Vibrations and Oscillations are the length of time needed for each cycle
– Period: T=1/f
– Frequency: 1/T
• Equilibrium Point is where the net force equals zero
• The natural frequency of a system resonates with large amplitude
• Two types of waves
– Transverse: where the vibration of the medium is perpendicular to the motion
of the wave produced.
• Only in material with rigidity, not in fluid because molecules would slip into one
another
– Longitudinal: when the vibration of the medium is along the same direction as
the motion of the wave.
• Can move through most materials because the materials can be compressed and have
restoring forces.
Summary Continued
• Periodic Wave
– all pulses have the same size and shape
– Wave pattern repeats itself over a distance of 1 wavelength
and 1 period
• Wavelength: the shortest repetition length for a
periodic wave, the distance from crest to crest or
trough to trough
– Crest: peak point of a wave disturbance
– Trough: low point of wave disturbance
• Wave Speed:
– Multiply the wavelength by the frequency or divide the
wavelength by the period
v= f
or
v=/T
Summary Continued
• Standing Waves: when there is an interference pattern
produced by two waves of equal amplitude and
frequency traveling in opposite directions
• Node: A position on a standing wave or interference
pattern where there is no movement (the amplitude is 0).
• Antinode: a position in a standing wave or interference
pattern where there is maximal movement (the
amplitude is maximum)
• Harmonics: frequencies that have a whole-number
multiple of the fundamental frequency
– The lowest resonant frequency for an oscillating system
Problem Areas
• Force and acceleration always
point towards the equilibrium
point.
• Waves:
– The speed of the pulse doesn’t
depend on its size or shape or
the manner in which it was
created (in a spring).
• They key determinants are tension
in the object (rope, spring) and the
mass of the object.
– Pieces or particles in a wave
move perpendicular to the
motion of the wave not along it.
They move up and down within
it.
White arrows show which
way the force and
acceleration point.
Conceptual Problem
Conceptual Question #4
A mass is oscillating up and down on a
vertical spring. When the mass is below
the equilibrium point and moving down,
what direction is its acceleration? Is the
mass speeding up or slowing down?
Answer:
a.) The acceleration is in the upward
position.
b.) The mass is slowing down.
Exercise
12. A girl with a mass of 40 kg is swinging from a
rope with a length of 2.5 m. What is the
frequency of her swinging?
Plug and Chug:
What we know:
T= 2π√(L/G)
F=1/T
=2
T of a pendulum
π√(2.5m/10m/s2)
= 2π√(L/G)
= 2 π(.5s)
= 1 π or just π
rope length = 2.5
T= π = 3.14
m
F = 1/T
weight = 40 kg
= 1/π seconds
(useless
= 0.318 (1/sec)
information)
-2
=
3.18
x
10
2
g = 10m/s
cycles/ second
Pictures found from:
• http://commons.wikimedia.org/wik
i/Main_Page
• http://www.physicsclassroom.com/
Class/waves/wavestoc.html
• http://id.mind.net/~zona/mstm/phy
sics/waves/partsOfAWave/wavePar
ts.htm